# Little Help with a Calc Question

#### americanangel

##### Senior Member
7+ Year Member
15+ Year Member
Okay I'm stuck on this for my calc II class...
integral of (x^3)(e^-x^2) and integral of (x^3)(2+x)^(5/2)

5+ Year Member
15+ Year Member

#### americanangel

##### Senior Member
7+ Year Member
15+ Year Member
Great site but i need to show work?? Any ideas how to get the answer?

#### Cerberus

##### Heroic Necromancer
15+ Year Member
damn, its been too long since calc two. Looks like integration by parts and substitution though.

#### americanangel

##### Senior Member
7+ Year Member
15+ Year Member
yeah that is what i was thinking but i keep getting these freaky integrals that dont match the real answer!!!

any ideas welcome!!!

#### Cerberus

##### Heroic Necromancer
15+ Year Member
Ok, i'll do the first one.

int(x^3)(e^-x^2)dx

let u=x^2

then

int[u*x*e^(-u)dx]
and dx = du*1/(2x)

so

int[u*x*e^(-u)(1/(2x)du) = 1/2*int[u*e^(-u)du]

by integration by parts:

1/2*int[u*e^(-u)du] = 1/2[-u*e^(-u) - int[1*e^(-u)du] = -1/2*u*e^(-u) + 1/2e^(-u) = -1/2*x^2*e^(-x^2) + 1/2e^(-x^2) = e^(-x^2)*(1-x^2)/2

#### americanangel

##### Senior Member
7+ Year Member
15+ Year Member
oh cool...that found my mistake...i did u=x instead of x^2
why i did that I dont know but at least I straightened that out!!!

thanks so much for that!!!
i really appreciate it!!!

#### kels

##### Member
10+ Year Member
For the second one, just substitute u=x+2. So you'll have (u-2)^3*u^(5/2). Expand the first term (u-2)^3 and you'll get something slight messy, but then you can multiply tern by term with u^(5/2), so you'll have a long polynomial with terms like u^(11/2). Then you can integrate those individually, like 12/13*u^(13/12).